Design and analysis of rigid and compliant mechanisms doctor of philosophy major mechanical engineering

The first objective was to investigate the effect of design parameters such as clearance size, material characteristic, friction in revolute clearance joints, driving speed, journal and

國 立 高 雄 科 技 大 學

機械工程系博士班

博士論文 剛性與柔順機構的設計與分析

Design and Analysis of Rigid and Compliant

Mechanisms

研究生：黃裕泰 指導教授 ：黃世疇 教授

中華民國 108 年 6 月

A dissertation Submitted to Department of Mechanical Engineering National Kaohsiung University of Science and Technology

in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

in Mechanical Engineering

June 09, 2019 Kaohsiung, Taiwan, Republic of China 中華民國 108 年 6 月 9 日

摘 要

本論文研究第一目標為探討多剛體機構接頭的設計參數，如間隙尺寸，材料特性，轉動間隙接頭摩擦，運轉速度，軸頸與軸承半徑等對其動態反應之影響；第二個目標為設計新型撓性鉸鏈接頭，以改善這些傳統接頭的缺點。

首先設計一個具二個滑塊與七個轉動間隙接頭的曲柄滑塊機構，研究中以有限元素法 ANSYS 分析該機構的動態特性。其次設計撓性鉸鏈的橋式柔性機構與張力位移放大器，然後以有限元素法 ANSYS 分析其輸出位移與輸出應力。文中應用田口方法，灰色關聯分析，熵測量技術，回歸方程與人工神經網絡等方法分析各機構之最佳化組合參數。

研究結果顯示，這些參數對曲柄滑塊機構的動態反應有顯著影響。加速度與

）與 106.854（N），加速度誤差為 3.92

％，接觸力誤差為 9.99％。橋式柔性機構撓性鉸鏈的設計參數最佳化及實驗結果一致，顯示其對輸出位移與輸出應力均有顯著影響。分析得到的最佳位移放大率，田口方法為 71.2，回歸方程為 71.05，人工神經網絡為 79.21。最佳輸出應力結果，田口方法為 73.44 MPa，回歸方程為 76.116 MPa，人工神經網絡為 73.362

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MPa。實驗結果與模擬誤差為 4.895％，田口方法誤差為 12.64％，回歸方程誤差

為 3.94％，人工神經網絡誤差為 13.83％。

有限元素與最佳化結果顯示設計參數對採用撓性鉸鏈的張力位移放大器的輸出位移和輸出應力均有顯著影響。對於田口方法，最佳輸出位移和輸出應力結果

為 0.6938mm 與 52.314MPa；灰色關聯分析為 0.6040mm 與 53.561MPa。其最佳位移放大率，田口方法為 69.38，灰色關聯分析為 60.4。

關鍵字：轉動間隙接頭，橋式柔順機構，張力位移放大器，田口方法，回歸方程，灰色關聯分析，人工神經網絡

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Design and Analysis of Rigid and Compliant Mechanisms

Department of Mechanical Engineering National Kaohsiung University of Science and Technology

Abstract

This study concludes two primary objectives The first objective was to investigate the effect of design parameters such as clearance size, material characteristic, friction in revolute clearance joints, driving speed, journal and bearing radius on the dynamic response of joints of rigid multibody mechanism The second objective was to design a new type flexure hinge joint to improve the drawbacks of these traditional joints

First of all, a slider-crank mechanism (SCM) with two sliders and seven revolute clearance joints was designed The behavior dynamic of this mechanism was obtained

by using finite element method in ANSYS Second, a bridge-type compliant mechanism and tensural displacement amplifier employing flexure hinge was designed And then output displacement and output stress were achieved by FEM in static structural of ANSYS The Taguchi method, Grey relational analysis, entropy measurement technique, regression equation and artificial neural network were applied to optimize three mechanisms and determine optimal combination parameters

The simulation and optimization results demonstrated that these design parameters have significantly affected on dynamic response of a slider-crank mechanism The optimal results of acceleration and contact force are 186.45 (m/s2) and 106.854 (N) respectively, with a 3.92% error for acceleration and 9.99% for contact force The simulation, optimization and experiment results are good agreed with design parameters

of a bridge-type compliant mechanism flexure hinge have significantly influenced on

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displacement and stress The optimal displacement amplification ratio obtained was 71.2, 71.05, and 79.21 by the Taguchi method, regression equation and artificial neural network, respectively The optimal stress results obtained were 73.44 MPa, 76.116 MPa and 73.362 MPa by the Taguchi method, regression equation and artificial neural network, respectively The deviation error between experiment and simulation, Taguchi method, regression equation, artificial neural network is 4.895%, 12.64%, 3.94%, 13.83%, respectively

The FEM and optimization results are line with each other with design parameters have significantly influenced on displacement and stress of a tensural displacement amplifier employing flexure hinge The optimal displacement and stress results were obtained by Taguchi method, grey relational analysis are 0.6938 mm and 52.314 MPa, 0.6040 mm and 53.561 MPa, respectively The optimal displacement amplification ratio was obtained 69.38 for TM and 60.4 for GRA

Keywords: Revolute clearance joint, Bridge-type compliant mechanism, Tensural

displacement amplifier, Taguchi method, Regression equation, Grey relational analysis, Artificial neural network

In addition, I would like to choose this opportunity to indicate my sincere thanks

to the members of the Computer Aided Engineering Application and Design LAB has helped me very enthusiastic during my time at National Kaohsiung University of Science and Technology

Last but not least, I would like to acknowledge my mother Thi Be Nguyen who helped, raised and inspired me through my graduate study I would like to thank my brothers, sisters for their love to my academic pursuit

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Contents

摘 要 i

Abstract iii

Acknowledgments v

Contents vi

List of Tables x

List of Figures xii

Nomenclature xvii

Latin symbols xvii

Greek symbol xviii

Abbreviations xviii

Chapter 1 Introduction 1

1.1 Overview 1

1.2 Advantages of rigid multibody and compliant mechanisms 2

1.2.1 Advantages and disadvantages of rigid multibody 2

1.2.2 Advantages of compliant mechanisms 3

1.3 Application of rigid multibody and compliant mechanisms 3

1.3.1 Application of rigid multibody mechanisms 3

1.3.2 Application of compliant mechanisms 5

1.4 Motivations, scope and objectives of the dissertation 8

1.4.1 Motivations 8

1.4.2 Scopes 9

1.5 Literature Reviews 10

1.5.1 Computational Methods for rigid and compliant Mechanisms 10

1.5.2 Optimization Methods for rigid and compliant Mechanisms 13

1.6 Organization of the dissertation 14

Chapter 2 Introduction kinematic joints and flexure hinge 15

2.1 Kinematic joints 15

2.2 Revolute clearance joint model 17

2.3 Translation joint 18

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2.4 Flexure hinge 18

Chapter 3 Dynamic and static analysis of rigid multibody and compliant mechanism by using finite element method 20

3.1 Dynamic analysis of a slider-crank mechanism with two sliders and revolute clearance joints by using finite element method 20

3.1.1 Introduction 20

3.1.2 Advantages and application of slider-crank mechanism with two sliders and revolute clearance joints 21

3.1.3 Finite element method 21

3.1.4 Effect analysis of clearance size 22

3.1.5 Effect analysis of bearing length 29

3.1.6 Effect analysis of radius of journal 31

3.1.7 Effect analysis of different of quantity of revolute clearance joints 32

3.1.8 Effect analysis of material 36

3.2 Static analysis for a bridge-type compliant mechanism flexure hinge using FEM in ANSYS 37

3.2.1 Introduction 37

3.2.2 Analysis finite element method 38

3.2.3 Advantages and applications of a bridge-type compliant mechanism flexure hinge 39 3.2.4 Effect analysis of input body length 39

3.2.5 Effect analysis of thickness of flexure hinge 40

3.2.6 Effect analysis of incline angle between of two flexure hinges 41

3.2.7 Effect analysis of width of flexure hinge 42

3.3 Effect analysis of design parameters to displacement and stress of a tensural displacement amplifier employing flexure hinges by using finite element method 42

3.3.1 Introduction 42

3.3.2 Finite element method 43

3.3.3 Advantages and applications of a tensural displacement amplifier employing flexure hinges 44

3.3.4 Influence analysis of thickness of the mechanism 44

3.3.5 Influence analysis of thickness of flexure hinge 45

3.3.6 Influence analysis of incline angle between two flexure hinges 45

3.3.7 Influence analysis of width of mechanism 46

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3.3.8 Analytical Influence of width of flexure hinge 47

3.4 Summary 48

Chapter 4 Application of multi-objective optimization methods to optimize design parameters for rigid and compliant mechanisms 50

4.1 Description of Taguchi method and regression equation 50

4.2 Description of grey relational analysis with Entropy measurement technique 50

4.3 Description of Artificial neural network 53

4.4 Statistical analysis 54

4.5 Dynamic optimization of a slider-crank mechanism by using Taguchi method and grey relational analysis 54

4.5.1 Simulation Preparation 54

4.5.2 Signal to noise (S/N) ratios analysis 56

4.5.3 Analysis of variance (ANOVA) of simulation 58

4.5.4 Regression analysis 59

4.5.5 Grey relational grade analysis 60

4.5.6 Predicted optimization 62

4.6 Optimization displacement amplification ratio of a bridge-type compliant mechanism by using Taguchi method and artificial neural network 65

4.6.1 Simulation preparation 65

4.6.2 S/N ratios analysis 66

4.6.3 ANOVA for output response 67

4.6.4 Regression equation 68

4.6.5 Artificial neural network 72

4.6.6 Predicted optimization 76

4.6.7 Experimental verification 78

4.7 Optimization of a tensural displacement amplifier employing flexure hinges using Taguchi method and grey relational analysis 79

4.7.1 Simulation preparation 79

4.7.2 Signal to noise (S/N) ratios analysis 81

4.7.3 Analysis of variance (ANOVA) of simulation 83

4.7.4 Regression equation 85

4.7.5 Grey relational grade analysis 90

4.7.6 Predicted optimization 94

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4.8 Summary 96

Chapter 5 Conclusions and Future Works 98

5.1 Conclusions 98

5.2 Contributions 99

5.3 Suggestion for Future Works 100

References 102

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List of Tables

Table 3 1 Simulation parameters 21

Table 3 2 Mechanical properties of material 38

Table 4 1 Parameters and their levels 55

Table 4 2 Experimental results and S/N ratio values 55

Table 4 3 Response table for signal to noise ratios 57

Table 4 4 Response table for signal to noise ratios 57

Table 4 5 Results of ANOVA for acceleration 58

Table 4 6 Results of ANOVA for contact force 59

Table 4 7 Response table for means of acceleration 60

Table 4 8 Response table for means of contact force 60

Table 4 9 Grey relational data, GRC, GRA and rank of GRG 60

Table 4 10 Response table for the mean GRG for each parameter level 61

Table 4 11 ANOVA results for GRG 62

Table 4 12 Comparison between predictions of Taguchi method and FEM 64

Table 4 13 Comparison between forecast of grey relational grade and FEM 64

Table 4 14 Parameters and their levels 65

Table 4 15 Orthogonal arrays, FEM results and S/N ratio for output response 65

Table 4 16 Response table for S/N ratios for displacement 66

Table 4 17 Response table for signal to noise ratios for stress 67

Table 4 18 ANOVA for displacement 68

Table 4 19 ANOVA for stress 68

Table 4 20 Design parameters and results for the testing simulation of DI 74

Table 4 21 Design parameters and results for the testing simulation of stress 75

Table 4 22 Statistical analysis results for predicted regression model 75

Table 4 23 Statistical analysis results for ANN model 75

Table 4 24 Response table for means of displacement 76

Table 4 25 Response table for means of stress 76

Table 4 26 Compare the regression and ANN results with TM results 78

Table 4 27 Parameters and their level 79

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Table 4 28 Orthogonal array and results 80

Table 4 29 Response table for S/N ratios for DI characteristic, larger is better 82

Table 4 30 Response table for means for displacement characteristic 82

Table 4 31 Response table for S/N ratios for equivalent stress characteristic 82

Table 4 32 Response table for means for equivalent stress characteristic 83

Table 4 33 ANOVA results for output displacement 84

Table 4 34 Analysis of variance for stress 84

Table 4 35 The large and the smaller is the better of DI and ST value, deviation, GRC, GRG and rank of GRG 91

Table 4 36 The average value of GRG 92

Table 4 37 ANOVA for GRG 93

Table 4 38 Compare between predicted value and optimal values 95

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List of Figures

Figure 1 1 Optimization of the flexible rod in a slider-crank mechanism [1] 2

Figure 1 2 (a) Rigid slider-crank mechanism, (b) Partly compliant mechanism, (c) Pseudo-rigid body model of compliant mechanism [2] 2

Figure 1 3 A two stage reciprocating compressor transmission mechanism with joint clearance [3] 4

Figure 1 4 Balancing shaft arrangement for an in-line four-cylinder engine [4] 4

Figure 1 5 Constitution of the transmission mechanism for the closed high 5

Figure 1 6 Compliant mechanisms: (a) Shampoo cap, (b) Bottle cap, (c) Hair pin 6

Figure 1 7 Prototype of the compliant gripper in its inactive mode (left) and gripping mode (right) [7] 6

Figure 1 8 Compliant scissors-forceps design [8] 7

Figure 1 9 Design of finger mechanism with contacting aided compliant mechanism [9] 7

Figure 1 10 Actuator principle with adjustable stiffness [10] 7

Figure 1 11 Schematics showing the structure of micro-cantilever system, the close-up of flexure hinge array, and actuation principle including states (a) before actuation and (b) after actuation [11] 8

Figure 2 1 Revolute joint 15

Figure 2 2 Cylindrical joint 15

Figure 2 3 Translation joint 16

Figure 2 4 Slot joint 16

Figure 2 5 Universal joint 16

Figure 2 6 Spherical joint 17

Figure 2 7 Planar joint 17

Figure 2 8 Revolute imperfect joint 18

Figure 2 9 Three shape flexure hinge [36, 64] 18

Figure 2 10 Geometric parameters and loads of the FHs [36, 64] 19

Figure 2 11 T-shape flexure hinge mechanism [65] 19

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Figure 3 1 Slider-crank mechanism, 1 1st connecting rod, 2 2nd connecting rod, 3 1st ray, 4 1st slider, 5 2nd ray, 6 Crank, 7 Motor, 8 Base, 9 2nd slider, 10 Rotation

of motor control and 11 DC 20

Figure 3 2 Projection of a mechanism on the oxy planar 20

Figure 3 3 Set up finite element and boundary condition in ANSYS 22

Figure 3 4 Velocity of the first slider with different CS 23

Figure 3 5 Acceleration of the first slider with different CS 24

Figure 3 6 Velocity of the second slider with different clearance size 24

Figure 3 7 Acceleration of the second slider with different clearance size 25

Figure 3 8 The contact force (CF) in the first RCJ R1 with different CS 25

Figure 3 9 The CF in the second RCJ R2 with different CS 26

Figure 3 10 The CF in the third RCJ R3 with different CS 26

Figure 3 11 The CF in the fourth RCJ R4 with different CS 27

Figure 3 12 The CF in the fifth RCJ R5 with different CS 27

Figure 3 13 The CF in the sixth RCJ R6 with different CS 27

Figure 3 14 The CF in the seventh RCJ R7 with different CS 28

Figure 3 15 The CF in the first translation joint T1 with different CS 28

Figure 3 16 The CF in the second translation joint T2 with different CS 29

Figure 3 17 Velocity graph of two sliders 30

Figure 3 18 Acceleration of two sliders 30

Figure 3 19 The contact force in RCJ and translation joint (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7, (h) T1, (i) T2 31

Figure 3 20 The velocity of two sliders with different journal radius 32

Figure 3 21 The acceleration of two sliders with different journal radius 32

Figure 3 22 The CF in RCJs and TJs (a) For R1, (b) For R2, (c) For R3, (d) For R4, (e) For R5, (f) For R6, (g) For R7, (h) For T1, (i) For T2 32

Figure 3 23 Velocity of the first slider with different amount of RCJs 33

Figure 3 24 Acceleration of the first slider with different amount of RCJs 33

Figure 3 25 Velocity of the second slider with different amount of RCJs 33

Figure 3 26 Acceleration of the second slider with different amount of RCJs 34

Figure 3 27 CF in the 1st RCJ (R1) with different quantity of RCJs 34

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Figure 3 28 CF in the 2nd RCJ (R2) with different number of RCJs 34

Figure 3 29 CF in the 3rd RCJs (R3) with different number of RCJs 34

Figure 3 30 CF in the 4th RCJ (R4) with different number of RCJs 34

Figure 3 31 CF in the 5th RCJ (R5) with different number of RCJs 35

Figure 3 32 CF in the 6th RCJ (R6) with different number of RCJs 35

Figure 3 33 CF in the 7th RCJ (R6) with different number of RCJs 35

Figure 3 34 CF in the 1st TJ (T1) with different number of RCJs 35

Figure 3 35 CF in the 2nd TJ (T2) with different number of RCJs 35

Figure 3 36 Accelerations of two sliders with different material and CS= 0.3 mm 36

Figure 3 37 CF in 7 RCJs and 2 TJs with different material and CS of 0.3 mm (a) CF of R1; (b) CF of R2; (c) CF of R3; ((d) CF of R4; (e) CF of R5; (f) CF of R6;(g) CF of R7; (f) CF of T1;(h) CF of T2 37

Figure 3 38 BTCMFH (a) 3D, (b) 2D, (c) Large view medium body and two FHs 38

Figure 3 39 (a) The meshed mechanism, (b) Fixed support and input DI for the mechanism 39

Figure 3 40 FEM result (a) DI and (d) ST for input with body length of 5 mm, (b) DI and (e) ST for input with body length of 10 mm, (c) DI and (f) ST for input with body length of 15 mm 40

Figure 3 41 FEM result (a) DI and (d) ST for flexure hinge thickness of 0.4 mm, (b) DI and (e) ST for flexure hinge thickness of 0.6 mm, (c) DI and (f) ST for flexure hinge thickness of 0.8 mm 41

Figure 3 42 FEM result (a) DI and (d) ST for incline angle of 0.7 degrees, (b) DI and (e) ST for incline angle of 1.0 degrees, (c) DI and (f) ST for incline angle of 1.3 degrees 41

Figure 3 43 FEM result (a) DI (d) ST for width of 2 mm, (b) DI and (e) ST for width of 4 mm, (c) DI and (f) ST for width of 6 mm 42

Figure 3 44 The tensural displacement amplifier compliant mechanism employing flexure hinge (a) 3D, (b) 2D 43

Figure 3 45 (a) The meshed model, (b) The mechanism was fixed and input DI 43

Figure 3 46 (a, b, c) is output deformation and (d, e, f) is output stress with different TOM (a, d) TOM of 10 mm, (b, e) TOM of 15 mm, (c, f) TOM of 20 mm 44

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Figure 3 47 (a, b, c) is output deformation and (d, e, f) is output stress with different TOFH (a, d) TOFH of 0.3 mm, (b, e) TOFH of 0.5 mm, (c, f) TOFH of 0.7 mm 45 Figure 3 48 (a, b, c) is output displacement and (d, e, f) is output tress with different incline angle (a, d) Incline angle of 0 degree, (b, e) Incline angle of 0.3 degree, (c,

f) Incline angle of 0.5 degree 46

Figure 3 49 (a, b, c) is output displacement, (d, e, f) is output stress with different WOM (a) WOM of 110 mm, (b) WOM of 115 mm, (c) WOM of 120 mm 47

Figure 3 50 (a, b, c) is output displacement, (d, e, f) is output stress with different WOFH (a, d) WOFH of 2 mm, (b, e) WOFH of 4 mm, (c, f) WOFH of 6 mm 48

Figure 4 1 Structure of ANN model in MATLAB with 5 input parameters, 11 neural in hidden layer and one output parameter 53

Figure 4 2 ANN training 53

Figure 4 3 S/N graph 57

Figure 4 4 Residual plot 59

Figure 4 5 Plotted GRG values for various experiments 62

Figure 4 6 Plotted GRG values for various experiments 62

Figure 4 7 S/N plot ((a) For output DI, (b) For output ST) 67

Figure 4 8 Comparison of forecasting values of RE and simulation values 69

Figure 4 9 Surface plots of displacement (a) Displacement vs x and y, (b) Displacement vs x and z, (c) Displacement vs x and t, (d) Displacement vs x and w, (e) Displacement vs y and z, (f) Displacement vs y and t, (g) Displacement vs y and w, (h) Displacement vs z and t, (i) Displacement vs z and w, (k) Displacement vs t and w 70

Figure 4 10 Surface plots of stress (a) Stress vs x and y, (b) Stress vs x and z, (c) Stress vs x and t, (d) Stress vs x and w, (e) Stress vs y and z, (f) Stress vs y and t, (g) Stress vs y and w, (h) Stress vs z and t, (i) Stress vs z and w, (k) Stress vs t and w 71

Figure 4 11 Comparison of simulation values and forecast values of ANN 72

Figure 4 12 Performance plot 72

Figure 4 13 Relationship between simulation and ANN model values for DI 73

Figure 4 14 Relationship between simulation and ANN model values for ST 74

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Figure 4 15 (a) Experimental setup, (b) Larger view BTCMFH 78

Figure 4 16 S/N plot 81

Figure 4 17 Means plot 82

Figure 4 18 Compare between simulation and predicted RE mode 85

Figure 4 19 Surface plot ((a) DI versus a and b, (b) DI versus a and c, (c) DI versus a and d, (d) DI versus a and e, (e) DI versus b and c, (f) DI versus b and d, (g) DI versus b and e, (h) DI versus c and d, (i) DI versus c and e, (k) DI versus d and e) 88

Figure 4 20 Surface plot ((a) ST versus a and b, (b) ST versus a and c, (c) ST versus a and d, (d) ST versus a and e, (e) ST versus b and c, (f) ST versus b and d, (g) ST versus b and e, (h) ST versus c and d, (i) ST versus c and e, (k) ST versus d and e) 90

Figure 4 21 (a) Plot GRG values for 27 simulations, (b) Response graph of GRG 92

Figure 4 22 Compare graph between GRG simulation and predicted model 94

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Nomenclature

Latin symbols

employing FH

displacement amplifier employing FH

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Greek symbol

Abbreviations

BTCMFH Bridge-type compliant mechanism flexure hinge